Can a Kallah who’s vort is during the 9 days buy a new dress for her vort during the three weeks?
It is controversial if we are allowed to buy and wear clothing that is special enough that it requires saying a shehechiyanu, therefore the Shulcha Aruch writes that it is preferable not to buy such a dress during the three weeks. However there is an option, to buy the dress and wear it on shabbos that is before the nine days, and then you can say shehechiyanu on it.
As a side point, we should not plan to make a vort for the nine days. Although if one got engaged during, or right before the nine days and the engagement party was made shortly afterwards it is permitted, because that would be considered a part of the actual engagement. However my understanding of your question is that the vort will only be two weeks after the engagement, and not a part of the actual engagement, but a planned party. To plan a party for the nine days is against the spirit of the time. The nine days are a time of mourning over the Bais Hamikdash, and the golus we are in and all of the problems that we have as a result of being in golus. The Mishna says “m’shenichnas Av mema’atim b’simcha” from when Av comes in we minimize our simcha” (until after T’.B’av). Aside from this, because it is the nine days, it cannot be a meal, and has to be kept simple. Additionally, there can’t be music or dancing. Regarding presents, although it is halachically permitted to give presents during the nine days, the minhag however is not to. In addition to this, although the chosson and kallah may wear shabbos clothes, however the rest of the (Ashkenazi) guest are going to have to come in weekday clothing.
 Magen Avrohom 551-21, Chayei Adm 133-14, Aruch Hahulchan 551-38, M:B 551-45
 R’ Y. Cahen shlit”a, Poskim.
 Taanis 26b, also see O:CH 551- 1,2, M:B 551-16,19, Aruch ashulchan 551-8.
 Kovetz Halachos (Bein Hamitzarim) 10-2.
 Mekor Chaim 552, Kol Hamisablim Aleha 17-6.
 Kol Hamisablim Alrha ibid, quoting Moadei Yishurun in the name of R’ Moshe Feinstein zt”l, and R’ S. Z Auerbach zt”l in Halichos Shlomo 14 ftnt.11.
 Rema 551-1.